Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-5820
Authors: Schweim, Dirk
Wittenberg, David
Rothlauf, Franz
Title: On sampling error in genetic programming
Online publication date: 3-May-2022
Language: english
Abstract: The initial population in genetic programming (GP) should form a representative sample of all possible solutions (the search space). While large populations accurately approximate the distribution of possible solutions, small populations tend to incorporate a sampling error. This paper analyzes how the size of a GP population affects the sampling error and contributes to answering the question of how to size initial GP populations. First, we present a probabilistic model of the expected number of subtrees for GP populations initialized with full, grow, or ramped half-and-half. Second, based on our frequency model, we present a model that estimates the sampling error for a given GP population size. We validate our models empirically and show that, compared to smaller population sizes, our recommended population sizes largely reduce the sampling error of measured fitness values. Increasing the population sizes even more, however, does not considerably reduce the sampling error of fitness values. Last, we recommend population sizes for some widely used benchmark problem instances that result in a low sampling error. A low sampling error at initialization is necessary (but not sufficient) for a reliable search since lowering the sampling error means that the overall random variations in a random sample are reduced. Our results indicate that sampling error is a severe problem for GP, making large initial population sizes necessary to obtain a low sampling error. Our model allows practitioners of GP to determine a minimum initial population size so that the sampling error is lower than a threshold, given a confidence level.
DDC: 330 Wirtschaft
330 Economics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 03 Rechts- und Wirtschaftswissenschaften
Place: Mainz
DOI: http://doi.org/10.25358/openscience-5820
Version: Published version
Publication type: Zeitschriftenaufsatz
License: CC BY
Information on rights of use: https://creativecommons.org/licenses/by/4.0/
Journal: Natural computing
2021
Publisher: Springer Science + Business Media B.V.
Publisher place: Dordrecht
Issue date: 2021
ISSN: 1572-9796
Publisher DOI: 10.1007/s11047-020-09828-w
Appears in collections:JGU-Publikationen

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